A note on $S$-Nakayama’s lemma
We propose an $S$-version of Nakayama's lemma. Let $R$ be a commutative ring, $S$ a multiplicative subset of $R,$ and $M$ be an $S$-finite $R$-module. Also let $I$ be an ideal of $R.$ We show that if there exists $t\in S$ such that $tM\subseteq IM,$ then$(t^\prime+a)M=0$ for some $t...
Збережено в:
| Дата: | 2020 |
|---|---|
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2020
|
| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/2332 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | We propose an $S$-version of Nakayama's lemma. Let $R$ be a commutative ring, $S$ a multiplicative subset of $R,$ and $M$ be an $S$-finite $R$-module. Also let $I$ be an ideal of $R.$ We show that if there exists $t\in S$ such that $tM\subseteq IM,$ then$(t^\prime+a)M=0$ for some $t'\in S$ and $a\in I.$ We also give an analog of Nakayama's lemma for a $w$-ideal and an $S$-$w$-finite $R$-module, where $R$ is an integral domain. Thus, we generalize the result obtained by Wang and McCasland [Commun. Algebra, 25, 1285–1306 (1997)]. |
|---|